Metanalysis of flow state on women caused by (stFemale)

Geiser C. Challco geiser@alumni.usp.br

Initial Variables and Loading Data

env <- "stFemale"
gender <- "women"
to_remove <- c('S11')
sub.groups <- c("age","ed.level","intervention","age:intervention",
                "ed.level:intervention","age:ed.level:intervention")
dat <- read_excel("../data/data-without-outliers.xlsx", sheet = "fss-env.gender-descriptive")
dat <- dat[!dat$study %in% to_remove, ]

leg <- read_excel("../data/data-without-outliers.xlsx", sheet = "legend")
## New names:
## • `` -> `...10`
leg <- leg[!leg$study %in% to_remove, ]

idx.e <- which(dat$env == env & dat$gender == gender)
idx.c <- which(dat$env == "control" & dat$gender == gender)

data <- data.frame(
  study = dat$study[idx.c],
  n.e = dat$N[idx.e], mean.e = dat$M.emms[idx.e], sd.e = dat$SD.emms[idx.e],
  n.c = dat$N[idx.c], mean.c = dat$M.emms[idx.c], sd.c = dat$SD.emms[idx.c]
)
for (cgroups in strsplit(sub.groups,":")) {
  data[[paste0(cgroups, collapse = ":")]] <- sapply(data$study, FUN = function(x) {
    paste0(sapply(cgroups, FUN = function(namecol) leg[[namecol]][which(x == leg$study)]), collapse = ":")
  })
}
data[["lbl"]] <- sapply(data$study, FUN = function(x) leg$Note[which(x == leg$study)])

Perform meta-analyses

m.cont <- metacont(
  n.e = n.e, mean.e = mean.e, sd.e = sd.e, n.c = n.c, mean.c = mean.c, sd.c = sd.c,
  studlab = lbl, data = data, sm = "SMD", method.smd = "Hedges",
  fixed = F, random = T, method.tau = "REML", hakn = T, title = paste("Flow state for",gender,"in",env)
)
summary(m.cont)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)
## S1                         0.6784 [ 0.0293; 1.3276]       12.8
## S2                         0.0758 [-0.4475; 0.5992]       19.7
## S3                        -0.3244 [-1.0470; 0.3982]       10.3
## S4                         0.7512 [-0.0340; 1.5363]        8.7
## S5                         0.3534 [-0.2481; 0.9549]       14.9
## S6                         0.6765 [-0.0622; 1.4152]        9.9
## S7                         0.2370 [-0.3729; 0.8470]       14.5
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.cont, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “age”

m.sg4sub <- update.meta(m.cont, subgroup = age, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)         age
## S1                         0.6784 [ 0.0293; 1.3276]       12.8  adolescent
## S2                         0.0758 [-0.4475; 0.5992]       19.7  adolescent
## S3                        -0.3244 [-1.0470; 0.3982]       10.3  adolescent
## S4                         0.7512 [-0.0340; 1.5363]        8.7       adult
## S5                         0.3534 [-0.2481; 0.9549]       14.9       adult
## S6                         0.6765 [-0.0622; 1.4152]        9.9       adult
## S7                         0.2370 [-0.3729; 0.8470]       14.5       adult
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2 adolescence
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Results for subgroups (random effects model):
##                     k    SMD            95%-CI  tau^2    tau    Q   I^2
## age = adolescent    3 0.1544 [-1.0524; 1.3613] 0.1185 0.3443 4.28 53.2%
## age = adult         4 0.4572 [ 0.0735; 0.8409]      0      0 1.49  0.0%
## age = adolescence   1 0.3530 [-0.4128; 1.1189]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   1.00    2  0.6056
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “ed.level”

m.sg4sub <- update.meta(m.cont, subgroup = ed.level, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)         ed.level
## S1                         0.6784 [ 0.0293; 1.3276]       12.8  upper-secundary
## S2                         0.0758 [-0.4475; 0.5992]       19.7  upper-secundary
## S3                        -0.3244 [-1.0470; 0.3982]       10.3  upper-secundary
## S4                         0.7512 [-0.0340; 1.5363]        8.7 higher-education
## S5                         0.3534 [-0.2481; 0.9549]       14.9 higher-education
## S6                         0.6765 [-0.0622; 1.4152]        9.9 higher-education
## S7                         0.2370 [-0.3729; 0.8470]       14.5          unknown
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2  upper-secundary
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Results for subgroups (random effects model):
##                               k    SMD            95%-CI  tau^2    tau    Q   I^2
## ed.level = upper-secundary    4 0.1963 [-0.4592; 0.8517] 0.0518 0.2277 4.48 33.0%
## ed.level = higher-education   3 0.5524 [ 0.0044; 1.1004]      0      0 0.77  0.0%
## ed.level = unknown            1 0.2370 [-0.3729; 0.8470]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   2.60    2  0.2732
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “intervention”

m.sg4sub <- update.meta(m.cont, subgroup = intervention, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)
## S1                         0.6784 [ 0.0293; 1.3276]       12.8
## S2                         0.0758 [-0.4475; 0.5992]       19.7
## S3                        -0.3244 [-1.0470; 0.3982]       10.3
## S4                         0.7512 [-0.0340; 1.5363]        8.7
## S5                         0.3534 [-0.2481; 0.9549]       14.9
## S6                         0.6765 [-0.0622; 1.4152]        9.9
## S7                         0.2370 [-0.3729; 0.8470]       14.5
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2
##                                                                   intervention
## S1                        Gender-stereotype color, ranking, badges, and avatar
## S2                        Gender-stereotype color, ranking, badges, and avatar
## S3                        Gender-stereotype color, ranking, badges, and avatar
## S4                        Gender-stereotype color, ranking, badges, and avatar
## S5                        Gender-stereotype color, ranking, badges, and avatar
## S6                        Gender-stereotype color, ranking, badges, and avatar
## S7                        Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs      Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Results for subgroups (random effects model):
##                                                      k    SMD            95%-CI  tau^2    tau    Q   I^2
## intervention = Gender-stereotype color, rankin ...   7 0.3200 [-0.0158; 0.6557] 0.0103 0.1013 7.20 16.6%
## intervention = Gender-stereotyped motivational ...   1 0.3530 [-0.4128; 1.1189]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   0.01    1  0.9363
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “age:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `age:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)
## S1                         0.6784 [ 0.0293; 1.3276]       12.8
## S2                         0.0758 [-0.4475; 0.5992]       19.7
## S3                        -0.3244 [-1.0470; 0.3982]       10.3
## S4                         0.7512 [-0.0340; 1.5363]        8.7
## S5                         0.3534 [-0.2481; 0.9549]       14.9
## S6                         0.6765 [-0.0622; 1.4152]        9.9
## S7                         0.2370 [-0.3729; 0.8470]       14.5
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2
##                                                                          age:intervention
## S1                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S2                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S3                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S4                             adult:Gender-stereotype color, ranking, badges, and avatar
## S5                             adult:Gender-stereotype color, ranking, badges, and avatar
## S6                             adult:Gender-stereotype color, ranking, badges, and avatar
## S7                             adult:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs     adolescence:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Results for subgroups (random effects model):
##                                                          k    SMD            95%-CI  tau^2    tau    Q   I^2
## age:intervention = adolescent:Gender-stereotype co ...   3 0.1544 [-1.0524; 1.3613] 0.1185 0.3443 4.28 53.2%
## age:intervention = adult:Gender-stereotype color,  ...   4 0.4572 [ 0.0735; 0.8409]      0      0 1.49  0.0%
## age:intervention = adolescence:Gender-stereotyped  ...   1 0.3530 [-0.4128; 1.1189]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   1.00    2  0.6056
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “ed.level:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `ed.level:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)
## S1                         0.6784 [ 0.0293; 1.3276]       12.8
## S2                         0.0758 [-0.4475; 0.5992]       19.7
## S3                        -0.3244 [-1.0470; 0.3982]       10.3
## S4                         0.7512 [-0.0340; 1.5363]        8.7
## S5                         0.3534 [-0.2481; 0.9549]       14.9
## S6                         0.6765 [-0.0622; 1.4152]        9.9
## S7                         0.2370 [-0.3729; 0.8470]       14.5
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2
##                                                                           ed.level:intervention
## S1                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S2                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S3                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S4                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S5                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S6                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S7                                 unknown:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs       upper-secundary:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Results for subgroups (random effects model):
##                                                               k    SMD            95%-CI  tau^2    tau    Q
## ed.level:intervention = upper-secundary:Gender-stereoty ...   3 0.1544 [-1.0524; 1.3613] 0.1185 0.3443 4.28
## ed.level:intervention = higher-education:Gender-stereot ...   3 0.5524 [ 0.0044; 1.1004]      0      0 0.77
## ed.level:intervention = unknown:Gender-stereotype color ...   1 0.2370 [-0.3729; 0.8470]     --     -- 0.00
## ed.level:intervention = upper-secundary:Gender-stereoty ...   1 0.3530 [-0.4128; 1.1189]     --     -- 0.00
##                                                               I^2
## ed.level:intervention = upper-secundary:Gender-stereoty ... 53.2%
## ed.level:intervention = higher-education:Gender-stereot ...  0.0%
## ed.level:intervention = unknown:Gender-stereotype color ...    --
## ed.level:intervention = upper-secundary:Gender-stereoty ...    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   2.29    3  0.5153
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Subgroup analysis by “age:ed.level:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `age:ed.level:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Flow state for women in stFemale
## 
##                               SMD            95%-CI %W(random)
## S1                         0.6784 [ 0.0293; 1.3276]       12.8
## S2                         0.0758 [-0.4475; 0.5992]       19.7
## S3                        -0.3244 [-1.0470; 0.3982]       10.3
## S4                         0.7512 [-0.0340; 1.5363]        8.7
## S5                         0.3534 [-0.2481; 0.9549]       14.9
## S6                         0.6765 [-0.0622; 1.4152]        9.9
## S7                         0.2370 [-0.3729; 0.8470]       14.5
## S10: Only use prompt msgs  0.3530 [-0.4128; 1.1189]        9.2
##                                                                                 age:ed.level:intervention
## S1                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S2                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S3                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S4                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S5                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S6                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S7                                     adult:unknown:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs     adolescence:upper-secundary:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 296
## 
##                         SMD           95%-CI    t p-value
## Random effects model 0.3202 [0.0360; 0.6044] 2.66  0.0323
## 
## Quantifying heterogeneity:
##  tau^2 < 0.0001 [0.0000; 0.4122]; tau = 0.0003 [0.0000; 0.6420]
##  I^2 = 2.8% [0.0%; 68.5%]; H = 1.01 [1.00; 1.78]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  7.21    7  0.4078
## 
## Results for subgroups (random effects model):
##                                                                   k    SMD            95%-CI  tau^2    tau
## age:ed.level:intervention = adolescent:upper-secundary:Gend ...   3 0.1544 [-1.0524; 1.3613] 0.1185 0.3443
## age:ed.level:intervention = adult:higher-education:Gender-s ...   3 0.5524 [ 0.0044; 1.1004]      0      0
## age:ed.level:intervention = adult:unknown:Gender-stereotype ...   1 0.2370 [-0.3729; 0.8470]     --     --
## age:ed.level:intervention = adolescence:upper-secundary:Gen ...   1 0.3530 [-0.4128; 1.1189]     --     --
##                                                                    Q   I^2
## age:ed.level:intervention = adolescent:upper-secundary:Gend ... 4.28 53.2%
## age:ed.level:intervention = adult:higher-education:Gender-s ... 0.77  0.0%
## age:ed.level:intervention = adult:unknown:Gender-stereotype ... 0.00    --
## age:ed.level:intervention = adolescence:upper-secundary:Gen ... 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   2.29    3  0.5153
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = paste0(gender,':',env))

Funnel Plot

m.cont <- update.meta(m.cont, studlab = data$study)
summary(eggers.test(x = m.cont))
## Eggers' test of the intercept 
## ============================= 
## 
##  intercept       95% CI    t    p
##       2.49 -2.76 - 7.74 0.93 0.39
## 
## Eggers' test does not indicate the presence of funnel plot asymmetry.
funnel(m.cont, xlab = "Hedges' g", studlab = T, legend=T, addtau2 = T)